Question: Multiply the following complex numbers, marked as blue dots on the graph: $[2] \cdot [5(\cos(\frac{7}{4}\pi) + i \sin(\frac{7}{4}\pi))]$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $2$ ) has angle $0$ and radius $2$ The second number ( $5(\cos(\frac{7}{4}\pi) + i \sin(\frac{7}{4}\pi))$ ) has angle $\frac{7}{4}\pi$ and radius $5$ The radius of the result will be $2 \cdot 5$ , which is $10$ The angle of the result is $0 + \frac{7}{4}\pi = \frac{7}{4}\pi$ The radius of the result is $10$ and the angle of the result is $\frac{7}{4}\pi$.